Gravitational lensing rarely produces high-mass outliers to the compact binary population

TL;DR

High-mass outliers in gravitational-wave data are not reliable indicators of strong gravitational lensing, as statistical fluctuations and intrinsic source rarity limit their effectiveness for constraining lensing optical depth.

Contribution

This paper demonstrates that high-mass outliers are not necessarily due to lensing and introduces a method to constrain lensing optical depth using gravitational-wave observations.

Findings

High-mass outliers are not strong indicators of lensing.

Constraints on lensing optical depth are currently weak.

Future data may better inform the distribution of cosmic lenses.

Abstract

All gravitational-wave signals are inevitably gravitationally lensed by intervening matter as they propagate through the Universe. When a gravitational-wave signal is magnified, it \emph{appears} to have originated from a closer, more massive system. Thus, high-mass outliers to the gravitational-wave source population are often proposed as natural candidates for strongly lensed events. However, when using a data-driven method for identifying population outliers, we find that high-mass outliers are not necessarily strongly lensed, nor will the majority of strongly-lensed signals appear as high-mass outliers. This is both because statistical fluctuations produce a larger effect on observed binary parameters than does lensing magnification, and because lensing-induced outliers must originate from intrinsically high-mass sources, which are rare. Thus, the appearance of a single lensing-induced outlier implies the existence of many other lensed events within the catalog. We additionally show that it is possible to constrain the strong lensing optical depth, which is a fundamental quantity of our Universe, with the detection or absence of high-mass outliers. However, constraints using the latest gravitational-wave catalog are weak$\unicode{x2014}$we obtain an upper limit on the optical depth of sources at redshift $1$ magnified by a factor of $5$ or more of $\tau(\mu\geq5,z=1)\leq 0.035 \unicode{x2014}$and future observing runs will not make an outlier-based method competitive with other probes of the optical depth. However, the full inferred population of compact binaries may be more informative of the distribution of lenses in the Universe, opening a unique opportunity to access the high-redshift Universe and constrain cosmic structures.